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The diffuse supernova neutrino background (DSNB)—a probe of the core-collapse mechanism and the cosmic star-formation history—has not been detected, but its discovery may be imminent. A significant obstacle for DSNB detection in Super-Kamiokande (Super-K) is detector backgrounds, especially due to atmospheric neutrinos (more precisely, these are foregrounds), which are not sufficiently understood. We perform the first detailed theoretical calculations of these foregrounds in the range 16–90 MeV in detected electron energy, taking into account several physical and detector effects, quantifying uncertainties, and comparing our predictions to the 15.9 live time years of pre-gadolinium data from Super-K stages I–IV. We show that our modeling reasonably reproduces this low-energy data as well as the usual high-energy atmospheric-neutrino data. To accelerate progress on detecting the DSNB, we outline key actions to be taken in future theoretical and experimental work. In a forthcoming paper, we use our modeling to detail how low-energy atmospheric-neutrino events register in Super-K and suggest new cuts to reduce their impact.

The Sun is a bright gamma-ray source due to hadronic cosmic-ray interactions with solar gas. While it is known that incoming cosmic rays must generally first be reflected by solar magnetic fields to produce outgoing gamma rays, theoretical models have yet to reproduce the observed spectra. We introduce a simplified model of the solar magnetic fields that captures the main elements relevant to gamma-ray production. These are a flux tube, representing the network elements, and a flux sheet, representing the intergranular sheets. Both the tube and sheet have a horizontal size of order 100 km and serve as sites where cosmic rays are reflected and gamma rays are produced. While our simplified double-structure model does not capture all the complexities of the solar-surface magnetic fields, such as Alfvén turbulence from wave interactions or magnetic fluctuations from convection motions, it improves on previous models by reasonably producing both the hard spectrum seen by Fermi Large Area Telescope at 1–200 GeV and the considerably softer spectrum seen by the High Altitude Water Cherenkov Observatory (HAWC) at near 10³GeV. We show that lower-energy (≲10 GeV) gamma rays are primarily produced in the network elements and higher-energy (≳few × 10 GeV) gamma rays in the intergranular sheets. Notably, the spectrum softening observed by HAWC results from the limited effectiveness of capturing and reflecting ∼10⁴GeV cosmic rays by the finite-sized intergranular sheets. Our study is important for understanding cosmic-ray transport in the solar atmosphere and will lead to insights into small-scale magnetic fields at the photosphere.